An analysis of world records for a variety of distances found that women have been improving about twice as quickly as men. And if that continues, the top female and male runners might start performing equally well between the years 2015 and 2055 in the 200-, 400-, 800-, and 1,500-meter events, according to a study. The findings were reported in a letter in the journal Nature.

"None of the current women's world-record holders at these events could even meet the men's qualifying standard to compete in the 1992 Olympic games," researchers Brian Wipp and Susan Ward wrote.

"However, it is the rates of improvement that are so strikingly different - the gap is progressively closing." But other researchers said they doubted the projections because they believed women's rate of improvement would slow.

Source: Journal staff and wire services, Milwaukee Journal, January 1992

Tasks

1. Construct a scatterplot of times in the 200-meters against year for the men's data. Construct a separate scatterplot for the women's data.

2. Calculate the correlation between men's times in the Olympic 200-meters and the Olympic year. Do the same for the women's times.

   Which gender's times in the Olympic 200-meters exhibit a stronger correlation with Olympic year?

3. Fit a least squares regression line to the data for men's times in the 200-meters. Draw the line on the men's scatterplot.

4. Fit a line to the data for women's times. Again, draw the line on the scatterplot.

5. Use the regression lines to make predictions for both men's and women's times in the Olympic 200-meters in the Olympic years 1996, 2000, and 2004.

6. At the Atlanta Olympics in 1996, Michael Johnson ran the 200-meters in 19.32 seconds (wow!). Use the prediction you calculated for 1996 to compute Johnson's residual.

   Now compute the prediction for women in 1988, when Florence Griffith-Joyner ran the 200-meters in 21.34 seconds. Calculate the residual for "Flo-Jo's" time.

   Use the two residuals to reach a conclusion about which of the two times was more "impressive" compared to the corresponding predictions. That is, which of Michael Johnson's 1996 time and Florence Griffith-Joyner's 1998 time was farther below what was predicted for that year?

7. Draw a third graph that displays the data for both men and women as well as the regression lines for men and women on the same plot.

8. Use the two regression lines you found to predict in what year men and women will run the same times in the 200-meters. Do you think it is realistic to expect that this will happen? Why or why not?

9. Write a letter to the editor of the Milwaukee Journal (the newspaper in which the article at the beginning of this handout appeared) explaining your conclusion about whether men and women will run the same times in the Olympic 200-meters "between the years 2015 and 2055" as the article states might happen.

   Note: You should not actually mail your letter to the Milwaukee Journal! But please write it as if you were going to mail it! Use language that an editor would understand, but refer to the statistical results you found to support your position.

The data are contained in the accompanying table.

Times for the Olympic 200 Meter Run

To illustrate the findings reported in the preceding article, you can analyze the winning times, in seconds, for the Olympic 200-meter run.